Question

For a real gas, if at critical conditions molar volume of gas is 8.2 litre at 3 atm, then critical temperature (in K) will be :

Answer 1

800 K

Answer 2

For a real gas obeying the van der Waals equation, the critical temperature ($T_c$) is related to critical pressure ($P_c$) and critical molar volume ($V_{m_c}$) by the formula: $T_c = \frac{8 P_c V_{m_c}}{3 R}$ Given $P_c = 3$ atm, $V_{m_c} = 8.2$ litre, and $R = 0.0821$ L atm mol$^{-1}$ K$^{-1}$. $T_c = \frac{8 \times 3 \times 8.2}{3 \times 0.0821} = \frac{8 \times 8.2}{0.0821} = 8 \times 100 = 800 \text{ K}$